A positive number is 30 less than its square. Find the number.

the positive number is equal to  6.

Step-by-step explanation:

from the question which says A positive number is 30 less than its square. Find the number.

let the number be "n"

and the square of the number = n²

So, we have  the expression to be

n = n²-30

n ²-30 -n =0

Re-arrange the equation

n²-n-30=0

the factors of -30 are 5 and -6

so we have

(n+5)(n-6)=0

n+5 =0

n = -5

or

n-6 =0

n = 6

therefore the number can either be -5 or 6.

note we are asked to find the positive number , so the positive number is 6

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560